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# Hypothesis testing problems

9.69 Late payment of medical claims can add to the cost of health care. An article (M. Freudenheim, "The Check in Not in the Mail," The New York Times, May 25, 2006, pp.C1, C6) reported that for one insurance company, 85.1% of the claims were paid in full when first submitted. Supposed the insurance company developed a new payment system in an effort to increase this percentage. A sample of 200 claims processed under this system revealed that 180 of the claims were paid in full when first submitted.

a. At the 0.05 level of significance, is there evidence that the proportion of claims processed under this new system is higher than the article reported for the previous system?
b. Compute the p-value and interpret its meaning.

9.70 The high cost of gasoline in the spring of 2006 had many people reconsidering their summer vacation plans. A survey of 464 Cincinnati-area adults found that 55 said they were planning on modifying or canceling their summer travel plans because of high gas prices ("Will You Travel?" The Cincinnati Enquirer, May 3, 2006, p.A10.)

a. Use the six-step critical value approach to hypothesis testing and a 0.05 level of significance to try to prove that the majority of Cincinnati-area adults were planning on modifying or canceling their summer travel plans because of high gas prices.
b. Use the five-step p- value approach to hypothesis testing and a 0.05 level of significance to try to prove that the majority of Cincinnati-area adults were planning on modifying or canceling their summer travel plans because of high gas prices.
c. Compare the results of (a) and (b).

9.72 A Wall Street Journal poll ("What's News Online," The Wall Street Journal, March 30, 2004, p.D7) asked respondents if they trusted energy-efficiency ratings on cars and appliances; 552 responded yes, and 531 responded no.

a. At the 0.05 level of significance, use the six-step critical the percentage of people who trust energy-efficiency rating differs from 50%.
b. Use the five-step p-value approach. Interpret the meaning of the p-value.

#### Solution Summary

The solution provides step by step method for the calculation of test statistic . Formula for the calculation and Interpretations of the results are also included.

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